theorem Th62: :: ZMODUL02:62

for R being Ring
for V being LeftMod of R
for v1, v2 being Vector of V st R = INT.Ring & V is Mult-cancelable holds
( v1 <> v2 & {v1,v2} is linearly-independent iff ( v2 <> 0. V & ( for a, b being Element of R st b <> 0. R holds
b * v1 <> a * v2 ) ) )